*Article* **Simulation of Evacuation from Stadiums and Entertainment Arenas of Different Epochs on the Example of the Roman Colosseum and the Gazprom Arena**

**Marina Gravit 1 , Ekaterina Kirik 2 , Egor Savchenko 3 , Tatiana Vitova <sup>2</sup> and Daria Shabunina 1, \***

	- e.savchenko@fakt-group.ru

**Abstract:** Space-planning decisions of two sports and entertainment arenas with large crowds—the Roman Colosseum (Italy) and the modern Gazprom Arena stadium (St. Petersburg, Russia)— were analyzed to compare the flow of people during evacuation by simulation. It was shown that the space-planning decisions of the Colosseum seem more advantageous compared with the Gazprom Arena in calculation of evacuation time and evacuation organization process: the capacity of the stairs of the Colosseum with a width of 2.8 m is comparable with the capacity of the Gazprom Arena's stairs (4 m). In the Colosseum the average specific flow is qaverage = 1.14 person/s/m, while in the Gazprom Arena the average specific flow is qaverage = 0.65 (with a march width of 2.6 m) and qaverage = 0.8 person/s/m (with a march width of 4 m). It was found that the Colosseum complies with current standards for on-time evacuation; while modern sports and entertainment arenas are currently designed with additional services, infrastructure, comfort and, in general, high commercialization. The antique arenas are currently being reborn and used for concerts and other public events, so the obtained results have practical significance.

**Keywords:** design; stadiums and arenas; evacuation time; safety; Colosseum; organizing evacuation; computer simulation

#### **1. Introduction**

Sports and entertainment stadiums with a large number of people are high-risk facilities. A source of hazard is the simultaneous presence of thousands of people in them. The greatest danger is posed by the operating conditions with the simultaneous targeted pedestrian movement, including the stadium outflow after events and the emergency evacuation, e.g., during a fire case. An important role belongs to the space-planning decisions of the structure: the size, configuration, and number of evacuation routes to leave the stands and the building in relation to the arena's capacity.

Computer simulation is widely used to analyze the infrastructure during public events and the operation of space-planning decisions [1,2]. For example, in Ronchi et al. [3], three scenarios of the evacuation of music festival locations with a capacity of 65 thousand people were explored. Simulations of pedestrian movement in the stands are considered in Was et al. [4], Wagner et al. [5], and Zhang et al. [6]. Simulation of the evacuation from the Wuhan Sports Center Stadium (one of the largest gymnasiums in China) was considered in Zong et al. [7]. In Wei et al. [8], the simulation technology of fire spread and evacuation in a large stadium was studied. In Kirik et al. [9,10], the authors presented the effects of different stadium features on evacuation times and densities, which were found using simulation.

**Citation:** Gravit, M.; Kirik, E.; Savchenko, E.; Vitova, T.; Shabunina, D. Simulation of Evacuation from Stadiums and Entertainment Arenas of Different Epochs on the Example of the Roman Colosseum and the Gazprom Arena. *Fire* **2022**, *5*, 20. https://doi.org/10.3390/fire5010020

Academic Editor: Alistair M. S. Smith

Received: 27 December 2021 Accepted: 29 January 2022 Published: 1 February 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Computer simulation provide numerical results for analyzing the object, verifying various hypotheses and obtaining reliable conclusions based on the simulation. Many works have been published aimed at the accurate reproduction of cultural heritage objects using digital technology. For example, [11] describes a digital 3D reconstruction of Sinhaya, a X–XIIth century Muslim suburb in the city of Zaragoza, as a result of which its exact models are obtained. The visualization is based on archaeological evidence from excavations and accurate historical documents. Digital reconstruction has helped to preserve some of the city's cultural heritage. In Papagiannakis et al. [12], a digital visualization of the 16th century Mosque of Hagia Sophia is presented in order to introduce virtual cultural heritage objects into an educational and recreational program. In Heigeas et al. [13], a modeling process is presented to produce a realistic crowd simulation in the ancient Greek agora of Argos. This paper considers the movement of crowds submitting to a common flow in a constrained environment. In Cain et al. [14], a study aimed to create a real-time interactive scenario in the ancient Roman Odeon in Aphrodisias based on historical sources is described. The results of the work present the development of the main scenarios of crowd movement.

Buildings with mass gatherings are not only the heritage of the contemporary world but similar arenas were also built in ancient times. The Roman Colosseum, which is the most famous structure of antiquity and was commissioned in 80 A.D., was built for gladiatorial games, mock naval battles, animal hunts, and the execution of criminals. The Colosseum is the largest amphitheater ever built, with an estimated capacity of 40,000 to 50,000 people [15,16]. The Colosseum was built of travertine stone, tuff, and brick, with marble as a facing material [17]. These materials are not combustible, but there was a fuel load in the building: on the upper tier, there were wooden masts and yards with sunshades on them; at the bottom (basement, under-stand galleries), there were wooden cages for animals, hay, fabrics, stretchers, baskets, etc. An open fire was used for lighting.

In Tan et al. [18] and Hernández [19], a goal was to reconstruct the Colosseum building using a computer model, and in Napolitano et al. [20], a model was created. A computer simulation of masonry in the stone structures of the Colosseum was used. In Croci [21], the weakness of the building concerning earthquakes is outlined. The influence of the space-planning decisions of the Colosseum on the evacuation time is partially considered in Gravit et al. [22]. According to [23], the Colosseum has such space-planning decisions that it is possible to fill and leave the amphitheater within a few minutes. It is estimated that due to the efficiency of the stairs, a full audience is able to leave the Colosseum in three minutes, which is disputed by the authors in [24]. This paper presents a digital reconstruction of the Colosseum to simulate crowd movement, which results in the identification of potential bottlenecks preventing rapid (timely) evacuation. As an effective evacuation scenario for the Colosseum, in [25], a comparison was made with one of the stadiums of modern times, the Beijing National Stadium ("Bird's Nest") built for the 2008 Olympic Games, on the TV show Time Scanners (on the National Geographic Channel). The experiment focuses on the ability of both stadiums to evacuate visitors in the shortest possible time: 1/8th of the Colosseum and the Bird's Nest Stadium were created to reproduce the stadium bowls, corridors, and stairs within seating. The experiment was conducted with two control measurements: full evacuation of people from the stands and full evacuation from the stadiums. According to the results of the first part of the experiment, it took 4 min for spectators to leave the stands in Beijing Stadium, while in the Colosseum during this time people were still in the stands, which means that the design of the exits and stands in the Bird's Nest Stadium is better in evacuation compared to the Colosseum. In the second part of the experiment, as the flow continues, the crowd density in the ancient amphitheater begins to decrease over time due to the configuration and width of the stairs, whereas in the modern stadium the flow begins to slow down and accumulate due to the integrated infrastructure. As a result, the last person left the Colosseum in 12 min 44 s and the last person left the Bird's Nest Stadium in 12 min 57 s. Thus, studying ancient objects and comparing them with modern objects is an actual task.

The purpose of this study was to simulate the space-planning decisions of two sports and entertainment arenas of different epochs: the Roman Colosseum (Italy) and Gazprom Arena (Russia) for a comparative analysis of the organization of pedestrian evacuation, with regard to the geometric characteristics of the stairs affecting the carrying capacity. The following tasks are set to achieve this purpose: to analyze the space-planning decisions of the considered arenas and on their basis to develop 3D models; to calculate and compare the movement of people on the stairs; to determine evacuation time, fields intensity of movement, and density of people.

#### **2. Materials and Methods**

#### *2.1. Evacuation Modelling*

In case of fire, the facility's smoke protection system plays a decisive role in ensuring safe evacuation conditions. The safe conditions are currently defined by the inequality (1):

$$t\_{\text{evac}} < \mathfrak{a} \; t\_{\text{block}} \tag{1}$$

where *tevac* is the time of the end of evacuation from the building area, *tblock* is the time of reaching the critical value by any dangerous fire factors, and 0 < *a* < 1 is a safety factor (for example, it equals 0.8 in Russia) [26].

The quantitative characteristics were obtained using the computer simulation of the movement of people (evacuation) in the Sigma FS (Russia) software package for the advanced fire and evacuation simulation [27,28]. The software was used to check the designs and organize pedestrian areas for the 2018 FIFA World Cup and the 29th Winter Universiade athletics facilities [9,29].

An individual flow model was built to simulate the evacuation. The model suggests the calculation of each person's position, including the positions of other people and obstacles on the plane, and allows one to specify individual characteristics, including the free movement velocity, projected area, path, and movement start time. The individual flow model is best suited for simulating the pedestrian traffic on facilities with stands.

At each time instant *t*, the position of each person is determined by the previous coordinate by the formula (2):

$$
\overrightarrow{\dot{\boldsymbol{x}}}\_{i}(t) = \overrightarrow{\dot{\boldsymbol{x}}}\_{i}(t - \Delta t) + \overrightarrow{\boldsymbol{v}}\_{i}(t)\Delta t,\ \dot{\boldsymbol{n}} = \overline{\mathbf{1},\mathbf{N}},\tag{2}
$$

where <sup>→</sup> *<sup>x</sup> <sup>i</sup>*(*<sup>t</sup>* <sup>−</sup> <sup>∆</sup>*t*) denotes the particle's position at the previous time step; <sup>→</sup> *v <sup>i</sup>*(*t*), *i* = 1, *N* is the particle's current speed measured in [m/s]; and ∆*t* is a time shift equal to 0.25 s.

A person's speed depends on density [30–32]. It is assumed that only conditions in front of the person influence on speed. It is motivated by the front-line effect (that is well pronounced while flow moves in open boundary conditions) in a dense mass of people, which results in the diffusion of the flow.

Thus, only density *Fi*(*α*ˆ) in the direction chosen is required to determine the speed. According to [30,33] the current velocity of the particle may be calculated, for example, by formula (3):

$$v\_{i}(t) = \begin{cases} v\_{i}^{0} \left(1 - a\_{l} \ln \frac{F\_{i}(\mathbb{A})}{F^{0}}\right) & F\_{i}(\mathbb{A}) > F^{0};\\ v\_{i'}^{0} & F\_{i}(\mathbb{A}) \le F^{0}. \end{cases} \tag{3}$$

where *F* 0 is the limit people density until which free people movement is possible (density does not influence on the speed of people movement); *a<sup>l</sup>* is the factor of people adaptation to current density while moving on *l th* kind way (*a*<sup>1</sup> = 0.295 is for horizontal way; *a*<sup>2</sup> = 0.4, for downstairs; *a*<sup>3</sup> = 0.305, for upstairs).

An individual flow model was built using the Sigma FS software to simulate the evacuation. The following individual characteristics of people were used in the calculation: 1. The average maximum velocity of a person's free movement was taken to be 1.66 m/s [33];


Simulation of the movement of each individual and the phenomena peculiar to the flow of people: merger, reshaping (spreading, compaction), the non-simultaneous merging of flows, formation and deformation of congestions, flow around turns, and movement in rooms with a developed internal layout, counter-flows, and intersecting flows are performed.

#### *2.2. Description of the Arena Designs—Gazprom Arena Stadium*

Gazprom Arena (Russia) is the most visited stadium in Eastern Europe, commissioned at the end of 2016 and hosting the 2018 FIFA World Cup and the 2020 UEFA European Football Championship [34].

According to the technical specifications of the building, a stadium bowl is designed for 68,000 seats, including temporary stands, which can be installed on the third- and sixthfloor stylobates. When the field is involved, the stadium capacity in the concert regime is increased to 80,000 people. The bowl consists of two (lower and upper) tiers. The height difference between the lower tier rows is almost 12 m. There are exits (safety hatches) to the second floor and to the inner stylobate located on the third floor (the attitude is +14.550). The lower bowl is almost symmetrical relative to the minor axis of the field. The height difference between the upper tier rows is almost 20 m. There are exits (safety hatches) to the fifth (+25,200) and sixth (+32,850) floors. The upper bowl can be considered symmetrical with respect to both axes. Figure 1 shows a north-eastern view of the Gazprom Arena and a 3D model of the Gazprom Arena (north-eastern view), built with Sigma FS software.

**Figure 1.** (**a**) Northeast side view of the Gazprom Arena stadium; (**b**) 3D model of the Gazprom Arena stadium (north-eastern view) built in the Sigma FS software.

The emergency exits from the building for the lower bowl audience are located mainly on the third floor (only the eastern-sector audience can exit outside directly from the second floor below the third-floor outer stylobate). The exit outside from the upper bowl is also located at the third-floor level. For this purpose, there are stairs accessed from the fifth and sixth floors. The audience members go out to the third floor outer stylobate from the stairs outside. There are 12 such access stairs along the stadium perimeter. In Figure 1, there are marching staircases STW with a number corresponding to the north-eastern quarter of the arena and running from the sixth floor. In addition, straight (no marches) stairs ST with a number are available to descend from the fifth floor directly to the third floor of the stylobate. The audience members descend from the third-floor stylobate to the grade.

In this study, the evacuation of the Gazprom Arena was considered from the upper bowl of the investigated quadrant. We assumed that the exit from the upper bowl would be the exit to the stylobate, located on the third floor, due to the space-planning similarity and comparable capacity of the Gazprom Arena and the Colosseum. Figure 2a shows the plan of the upper bowl of the north-eastern part of the Gazprom Arena, specifying the number of people in the stands. The numbers of people going to the fifth and sixth floors are shown, and the stairs that can be used to descend are indicated (STW1 and STW3). Figure 2b shows a plan of the fifth-floor under-stand space. Stairs accessible from the fifth floor to the third floor (STW1, STW2, and STW3) and straight descents directly to the third floor outer stylobate (ST1, ST2, and ST3) are marked. The arrows show the directions of movement from the hatches to the nearest exits from the floor; the numbers of people for whom the corresponding exit is the nearest one are indicated (the total number of people is 4454). The stairs are distributed around the fifth floor fairly uniformly. In this case, the loads on the adjacent stairs differ by a factor of up to 2. The stairs-to-sector ratio is 6/9. Figure 2c presents a plan of the sixth-floor under-stand space. The stairs accessible for descending from the sixth to third floor (STW1, STW2, and STW3) are shown. The arrows show the directions of movement from the hatches to the nearest exits from the floor; the numbers of people for whom the corresponding exit is the nearest one are indicated (the total number of people is 4692). The analysis of the sixth-floor plan shows that the number of stairs in it is twice as small as on the fifth floor, while the number of audience members on the former is greater. The stairs-to-sector ratio is 3/9. The stairs are nonuniformly distributed relative to the hatches, the loads on the stairs differ by a factor of more than 2, and the minimum load is twice as high as that on the fifth floor.

**Figure 2.** (**a**) Plan of the upper bowl of the north-eastern part of the Gazprom Arena and the number of people in the stands; (**b**) plan of the north-eastern part of the Gazprom Arena fifth floor; (**c**) plan of the north-eastern part of the Gazprom Arena sixth floor.

For further analysis, only stairs STW1, STW2, and STW3 are considered, since they are used by people descending from two (fifth and sixth) floors. In addition, the design of stairs STW1 is significantly different from that of stairs STW2 and STW3 (Figure 3). The quantitative data are given in Table 1.

31


**Table 1.** Loads on stairs STW1, STW2, and STW3 and their geometric dimensions.

The minimum path width for stairs STW1 is 1.5 times less than for the stairs STW2 and STW3, although the number of people evacuating on the stairs STW1 (2180) is comparable to the number evacuating on the stairs STW2 (1872) and STW3 (2592). The ratio between the discharge values for these stairs is the same. Calculating the stairs loading according to the nearest stairs principle, it is clear that the staircase with the lowest discharge value (STW1) on the sixth floor has an almost maximum load: the stairs take half of the northern part of the sixth floor. At the same time, the adjacent stairs STW2 with a discharge value greater by a factor of 1.5 are only accessed for two sectors located directly on the corner. The load on stairs STW1 on the fifth floor is reduced by the presence of exit ST1.

#### *2.3. Description of the Arena Designs—Colosseum*

There has still been no consensus among historians and architects about an antique amphitheater's design features and appearance. The characteristics that are important for the study and included in the three-dimensional computer model of the building to simulate evacuation and analyze the results obtained are considered. The computer model of the Colosseum is based on Durm's structural scheme [16]. During the simulation, the main attention is paid to the under-stand space, and the stairs for descending from the upper tiers since this part of the building affects the evacuation time the most.

The Colosseum central part is an oval stage surrounded by a flat strip of seats; the ratio between the major and minor axes of the entire building is 1.22. An oval cone with seats is around the arena. It is based on 80 parting walls directed radially inward and interconnected by ring walls and arched rows. Between them, there are a corresponding number of radially directed crossings and staircases; ring galleries stretching along the entire amphitheater between the ring walls and arcades connect walkways and stairs. The exterior galleries of the second and third floors serve as lounges. The gallery height on the floors is 10–11 m.

There are 80 arches along the outer perimeter that form 80 amphitheater entryways (Figure 4). The entrances/exits are located at the ground level (the so-called datum). Therefore, the evacuation can only occur top-down.

**Figure 4.** (**a**) Schematic of the Colosseum architectural design according to Durm's representations [16]; (**b**) schematic view of the Colosseum second floor (Gyuade) [16]; (**c**) fragment of the stairs.

The amphitheater can be conventionally divided into three tiers, each containing under-stand galleries, stands, and walkways to the seats (Figure 5).

**Figure 5.** Sigma FS software 3D models of the Colosseum.

The model was built assuming that the access to the ground-tier stands was mainly through the second floor; to the second-tier stands, through the third floor; and to the third-tier stands, through the fourth floor (the attitude of the latter is about +40,000). The first two tiers represent sequences of 20 stand rows, and the upper tier contains 16 rows. The data on the maximum arena capacity reported by different authors are inconsistent and vary between 40 and 50 thousand audience members simultaneously [16], so the conventional number of people is 48,000.

The Colosseum has the line-of-sight downstairs on both sides of each exit to the understand gallery (Figure 4b). The simulation considered 1/4 of the Colosseum (calculation sector), where 4 stairs are taken to evacuate people, which are located in this sector. The extreme stairs on two opposite sides of the calculation sector take the remainder of the flow for each subsequent sector. The stairs are uniformly distributed along the floor perimeter. The number of stairs is consistent with the number of exits to the under-stand space, i.e., it is equal to the number of tier sectors. The stairs path width along the axis of movement ranges from 2 m for descending from the upper tier of stands to the third floor to 4.5 m in the lower part.

#### *2.4. Initial Data for the Evacuation Simulation*

To compare the two arenas, a quarter of the Colosseum and a quarter of the Gazprom Arena's upper bowl are considered. This is justified by the symmetry of the Colosseum and the Gazprom Arena upper bowl with respect to both axes; in addition, the buildings have comparable capacities (12,000 and 9500 people, respectively), and the only way to evacuate is down the stairs.

Figures 6 and 7 show the 3D models built for the arenas. The Gazprom Arena computer model was built using modern drawings. The entire stadium was modeled and used not only within the limits of this study.

**Figure 6.** (**a**) The position of people in the stands of the Gazprom Arena before the evacuation; (**b**) the position of people during evacuation from the Gazprom Arena at the hundredth second from its beginning.

*Fire* **2022**, *5*, 20

**Figure 7.** (**a**) View from the side of the Colosseum; (**b**) view from the center of the arena; (**c**) view from the front of the building.

The Colosseum computer model is based on Durm's structural scheme [16]. The attention was mainly paid to the under-stand space, and the stairs for descending from the upper tiers since this part of the building affects the evacuation time the most. The arrangement of the stairs for descending from the upper tiers is approximately the same around the perimeter of the arena, so, when building the computer model, the approximate length and width of each unit path down from the upper floors and the number of paths (stairs) are provided.

Many geometrical dimensions of the interior space of the Colosseum were taken at a scale relative to the known dimensions given in the drawings. The descriptions provide limited data on the configuration of the stairs used to descend from the upper tier to the third floor. However, it is known that people from the upper tier merged into the streams of people from the corresponding sectors of the lower tier. Therefore, the stairs for descending from the upper-tier were conditionally restored to ensure the descent of a number of persons significant for further consideration in the general flow to the third floor. Each sector of the stands on each tier has a staircase for descending from the sector to the underlying floor, where people use the nearest stairs to descend further. The model includes 5 sectors. They are secured by 5 access staircases. In order to exclude boundary effects, the dynamics of human movement in the central part was analyzed, i.e., in the three central sectors and the four central staircases. For the same reason, the extreme sectors in the model are only half-filled (Figure 7b).

The computational domain involved the stands, under-stand galleries, and stairs. At the initial instant of time, people were in the stands or in the under-stand space. The evacuation of people from the building was simulated before exiting outside at the firstfloor level for the Colosseum and before exiting beyond the exterior perimeter to the stylobate for the Gazprom Arena.

#### **3. Results and Discussion**

#### *3.1. Comparative Analysis of the Arenas Using the Numerical Simulation of Human Movement*

Figure 8 shows a fragment of the Colosseum evacuation at the hundredth second from its beginning and mass gathering intensity field on the Colosseum third floor. Figure 9 shows the fields intensity of movement and crowding.

There were 7 calculations (scenarios) for the Gazprom Arena with different staircase loads STW1 and STW2-3. The last two scenarios (6 and 7) are proposed in the absence of flow control on the fifth and sixth floors with an uneven distribution of stairs, which is explained by the use of certain sectors for the needs of different client groups. The data on number *N* of the persons who passed the stairs, spent time *t*, and flow rate *Q*, determined by formula (4), are given in Table 2.

$$Q = \mathcal{N}/t\tag{4}$$

**Figure 8.** (**a**) Fragment of the Colosseum evacuation at the hundredth second from its beginning; (**b**) mass gathering intensity field on the Colosseum third floor.

**Figure 9.** (**a**) Field of total traffic intensity in seconds on the second and third floors of the Colosseum; (**b**) intensity field of crowding in seconds on the second and third floors of the Colosseum.


**Table 2.** Numerical characteristics of the Colosseum and Gazprom Arena.

According to Table 2, rows 1–4 do not account the remaining number of evacuees in the Colosseum, which are on the extreme staircases on two opposite sides of the calculation sector.

The data are given in columns 4 and 7 confirm the expected difference (by a factor of about 2) between the flow intensity estimates for stairs STW1 and STW2-3 because of the similar difference between the path widths. At similar numbers of persons, the evacuation time for stairs STW1 is twice as long as for stairs STW2-3.

It is worth noting that the capacity of the Colosseum stairs is comparable with that of stairs STW2-3 in the Gazprom Arena. Meanwhile, the staircase width in the Colosseum is smaller by a factor of ∼1.5. The construction of the stairs causes this effect. In the Colosseum, the height difference between the third and first floors is 22 m; in the Gazprom Arena, the height difference between the investigated sixth and third floors is 18.3 m. These values can be considered similar. The structure of the Gazprom Arena stairs was accurately reconstructed in the computer model. The main important features are that all the stairs connecting the upper floors are outside the bowl. There are eight 180◦ turns between the sixth and third floors (a stair flight has an average height difference of 2.1 m and an average slope of 30◦ ; the flight widths are given in Table 1).

The evacuation time for the considered part of the Gazprom Arena ranges from 520 to 2080 seconds and depends on the load of the stairs and can be regulated by the organisation of the human flow. The evacuation time from the Colosseum is 14.5 min, taken as the sum of the maximum time to leave the stairs of the sector (840 s) and the additional time to exit from the structure (30 s).

In order to assess the results obtained for the Colosseum, it should be noted that the interior space (in particular the staircases) has been reconstructed approximately. However, the space-planning decisions of the Colosseum floors, which is still accessible for research, and the data on the under-stand space structure and the axes lengths in the plan allow to consider the geometry of the Colosseum vertical connections used in the model to be sufficient for this study. In particular, the descent from the third to second floor was reconstructed as straight (without turns, its length is 21.5 m); it occupies the under-stand space of the second tier. The stair flights going down from the floors are codirected; to reach the next flight, one needs to make two 180◦ turns. There is one 180◦ turn between the second and first floors, and there are three turns to make in total when descending from the third and first floors; the average flight slope is 30◦ .

Table 3 generalizes the numerical characteristics of the investigated stairs for the two arenas. The Colosseum stairs are characterized by the highest specific flow (column 5). With conditionally the same length, slope, and height difference parameters, this fact is ensured by the layout of the Colosseum stairs, specifically, by the number of turns (column 6), which is twice as small as in the Gazprom Arena stadium. The result obtained is consistent with the data of a full-scale experiment [35], in which the movement downstairs in a nine-storied building was examined; there were 180◦ turns on the stairs, and the specific flow decreased with a decrease in the floor (and an increase in the number of turns).


**Table 3.** Summary table with the numerical characteristics of the Colosseum and Gazprom Arena stairs.

Thus, under other conditions, which can be assumed to be the same or slightly different for the investigated arenas, a key characteristic that determines the building evacuation rate was found to be the geometric characteristic of the stairs determining the number of 180◦ turns. The relation between the specific flow and the number of turns is nonlinear. In addition, as can be seen from rows 1 and 2 of column 5, the configuration of the stairs (Figure 3) also affects the flow rate. Table 4 shows the main geometric characteristics of the Colosseum and Gazprom Arena stairs.


**Table 4.** Summary table with the numerical characteristics of the Colosseum and Gazprom Arena stairs.

#### *3.2. Discussion*

The most reliable smoke protection methods are the use of optimal space-planning decisions of buildings and structures.

The Colosseum is an open structure, where, in case of fire, there are almost no obstacles for spreading the dangerous fire factors, including, first of all, smoke, in the under-stand space; therefore, the speed of evacuation from the building is a decisive factor. The high velocity of movement of people from the upper tiers is ensured by the escape routes maximally straightened using the optimal configuration of the stairs and providing each stand with its own downstairs and own exit from the building. In the Colosseum, the people gathering places with a density of 6 [person/m<sup>2</sup> ] and higher are the exits to the downstairs on the third floor (Figure 8b), since the capacity of these stairs is lower than the intensity of flows from the second and third tiers. Therefore, the time of mass gathering on the third floor can be minimized by the phased evacuation.

In the Gazprom Arena, the under-stand space is fenced off from the environment (in contrast to the bowl, which, in general, can be considered open). The smoke protection by design is implemented via walling off the staircases and making them smoke-free. The availability of downstairs in the Gazprom Arena upper bowl ranges within 1/3–2/3 on different floors. This leads to the discrepancy between the intensities of the suitable flow and the discharge values of the doors on the staircase and causes the long-term (up to 900 s) mass gathering (Table 4). The problem can be solved by organizing the phased evacuation. To enhance the efficiency of using the vertical lines, it is necessary to control the human flows on the fifth floor in order to relieve stairs STW1-likewise, which take a significant load in the south and north sectors of the sixth floor.

#### **4. Conclusions**

Currently, ancient arenas are being reborn: They are used for concerts and other public events, so research on the calculation of evacuation times from such structures is relevant and meaningful. In addition, the Colosseum is the prototype of most modern sports facilities in the present (Fisht Stadium (Sochi, Russia) and the Bird's Nest Stadium (Beijing, China)).

The evacuation process from Colosseum (Italy, Rome) and the Gazprom Arena (Russia, St. Petersburg) is investigated using pedestrian dynamics simulation. The effect of the design of evacuation paths on evacuation time(s) is studied, and the need to optimally organize evacuation (assist in loading stairs) is found.

According to results of investigation, the Colosseum design seems advantageous over the Gazprom Arena. The most significant difference is the higher stability and weak need of the evacuation process in the control factors. The key issue is the uniform distribution of vertical communication ways around the perimeter of the arena, the balance of the capacity of the escape routes and the intensity of the flow, which is also achieved due to the geometric features of the escape routes—the straighter the path, the higher the speed of movement.

The greatest intensity of human flows in the Colosseum is recorded on the third floor, because spectators are flocking here from the two tiers (second and third). There are also the longest crowds (the average duration is 200–250 s).

In the Colosseum, the high speed of movement of people from the tiers is realized by maximally straightened evacuation routes (staircase configuration and provision of each tribune with its own staircase). The stairwells at the Gazprom Arena are walled off and separated from the general volume of the stadium bowl, in particular, from the understands premises. The availability of staircases for the upper tier stands at the Gazprom Arena varies between 1/3 and 2/3 of the floors. The key characteristic determining the building's evacuation rate is the number of 180◦ turns.

According to the simulation results, the evacuation from the upper bowl of the Gazprom Arena to the stylobate of the 3rd floor ranges from 9 to 35 minutes. The evacuation depends on the location and load of the stairs, which is uneven and can be regulated by organising the flow of people. The evacuation from the Colosseum is 14.5 minutes, as the stairs are designed to be evenly loaded and symmetrically arranged. When the flow is organised appropriately in the Gazprom Arena, the structures have similar evacuation times. With an average march width of 2.8 m, the average specific flow qaverage = 1.14 person/s/m (in the Colosseum), and 0.65 and 0.8 person/s/m (in the Gazprom Arena on the STW1 and STW2-3 types of stairs, respectively).

The Colosseum is designed with large, long staircases using the principle of Vomitoria, which means eruption. This study proved the effectiveness of the stairs used in the Colosseum. In the construction of a structure in order to ensure the shortest possible evacuation time, this solution is the most effective. According to this study, the Colosseum complies with current standards for timely evacuation and can be operated as a modern sports and entertainment facility and host public events.

The main difference between modern sports and entertainment arenas is that they are designed with additional services, infrastructure, comfort and, in general, high commercialization, which has an impact on evacuation times and requires additional resources for the application of organizational management of the flow of the people.

**Author Contributions:** Conceptualization, M.G.; software, E.K.; investigation, T.V.; formal analysis, E.S.; data curation, D.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation under the strategic academic leadership program "Priority 2030" (Agreement 075-15-2021-1333 dated 30 September 2021).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** The authors would like to thank Nikolai Ivanovich Vatin, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia, for valuable and profound comments.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Review* **Influence of Natural Fire Development on Concrete Compressive Strength**

**Robert Kuehnen, Maged A. Youssef \* and Salah F. El-Fitiany**

Department of Civil and Environmental Engineering, Faculty of Engineering, Western University, London, ON N6A 5B9, Canada; rkuehnen@uwo.ca (R.K.); selfitia@uwo.ca (S.F.E.-F.) **\*** Correspondence: youssef@uwo.ca

**Abstract:** With increasing acceptance of performance-based design principles in the field of fire safety, it is imperative to accurately define the behaviour of materials during fire exposure. Real-world fire events, otherwise referred to as natural fires, are defined by four characteristics: heating rate, maximum temperature, exposure duration, and cooling rate. Each of these four characteristics influences concrete's behaviour in a different manner. In this paper, the available experimental work for concrete, tested at elevated temperatures, is examined to identify the influence of the four natural fire characteristics on concrete compressive strength. This review focuses on normal strength concrete tests only, omitting parameters such as unique additives and confinement. The intent is to provide a fundamental understanding of normal strength concrete. The findings show that maximum temperature and cooling rates have a significant influence on concrete strength. Exposure duration has a moderate impact, particularly at shorter durations. Variable rates of heating have minimal influence on strength. Detailed conclusions are provided along with review limitations, practical considerations for designers, and future research needs.

**Keywords:** natural fire; concrete strength; exposure duration; maximum temperature; heating rate; cooling rate

#### **1. Introduction**

In contrast with timber and steel construction, one of the primary advantages of using concrete as a building material is that it can withstand fire events without burning, melting, or needing additional protective materials. Concrete, however, is not completely unaffected by fire exposure. Studies on normal strength concrete (NSC) have shown that an exposure temperature of 600 ◦C can reduce concrete compressive strength by up to 55% [1].

There are a number of material properties that are known to affect concrete strength at elevated temperatures, such as ambient strength, aggregate type, water-cement ratio, additives, and prestress level. The influence of these properties is well investigated in the existing experimental work and detailed in numerous textbooks and literature-review publications [2,3]. Concrete strength is also affected by fire characteristics, such as: rate of heating, maximum temperature level, exposure duration, and rate of cooling [4]. The influence of these four fire characteristics is less thoroughly addressed in the existing literature.

It is imperative for designers to understand the behaviour of fires and its influence on concrete compressive strength. Existing performance-based models have shown that understanding these four fire characteristics is a necessary step to accurately modeling reinforced concrete beam and column behaviour [5]. By implementing the findings of this review into existing models, designers can produce performance-based solutions with increased confidence in safety, reliability, and efficiency.

**Citation:** Kuehnen, R.; Youssef, M.A.; El-Fitiany, S.F. Influence of Natural Fire Development on Concrete Compressive Strength. *Fire* **2022**, *5*, 34. https://doi.org/10.3390/fire 5020034

Academic Editor: Wojciech W˛egrzy ´nski

Received: 19 January 2022 Accepted: 24 February 2022 Published: 28 February 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **2. Natural Fire Definition**

Fire events are typically represented by temperature-time relationships, as shown in Figure 1. The term natural fire is used to define a fire event as it would occur in the real world. No two natural fires will ever be identical, as these fires are influenced by a wide range of compartment and environmental properties. Three examples of potential fire profiles are shown in Figure 1. Fire events can have high temperature over short duration, low temperature over long duration, or anywhere in between. ‐

**Figure 1.** Examples of natural fire temperature–time curves.

‐ ‐ ‐ ‐ To define a natural fire, four fire characteristics can be calculated: heating rate, maximum temperature, overall exposure duration, and cooling rate [4]. During the growth of a fire, variable rates of heating can occur, ranging from slow heating to almost instantaneous flashover. The rate of heating is greatly dependent on available oxygen and the presence of highly combustible materials. At the peak of a fire event, the value of the maximum temperature as well as its exposure duration vary based on reliability of fuel and oxygen supply. Once a fire begins to decay, variable rates of cooling can be present, ranging from slow air cooling in a smoldering compartment to rapid water cooling achieved by firefighting efforts. Each of these four fire characteristics plays a notable and different role in the deterioration of concrete strength. It is the influence of these characteristics on concrete strength that is evaluated in this paper.

#### **3. Available Experimental Work**

‐ ‐ ‐ The available experimental work features a wide range of testing parameters. To narrow the scope of this review, several concrete and testing parameters are controlled. Only tests with the following attributes have been reviewed in this paper: (a) unstressed tests, (b) unconfined tests, (c) unsealed tests, (d) ordinary Portland cement (no additives such as fly ash, silica, fibers, etc.), and (e) NSC with ambient strength less than or equal to 50 MPa. The intent of the control parameters is to focus the evaluation on basic NSC. Doing so highlights the influence of fire characteristics on behaviour and allows future researchers to identify when newly introduced parameters present unusual responses. Additionally, the majority of existing work is based on NSC, allowing for a wide range of sample data points.

In addition to the controlled parameters, there are other parameters that are known to affect compressive strength during fire exposure. These parameters include water-cement

ratio, aggregate-cementitious material ratio, aggregate type, size and content, geometric dimensions, and testing procedure [3]. Because there is so much variation in the existing experimental work, it is difficult to control all these parameters. Furthermore, the variation of these parameters is acceptable within the definition of NSC. To provide meaningful review, specific sections of this paper control the various parameters when possible, and when not possible, a selection of similar tests are averaged and presented for evaluation. 

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Table 1 shows a summary of the experimental tests investigated during this review. Full details are available in the referenced work. The required fire characteristics of each test, shown in Figure 2, are identified in the table. The concrete ambient strength ("*f'c,20*") and reported "aggregate" type are also recorded for additional context. "Testing time" refers to when the compressive strength of the sample was taken. A "residual" testing time indicates that testing occurred after the specimen cooled back to ambient temperature. A "hot" testing time indicates testing occurred while the sample was still at the maximum applied temperature.

**Figure 2.** Furnace heating profile during specimen testing.

For experimental work with a variable "heating rate", the average rate is provided in the table. A heating rate of "instant" indicates that the specimen was placed in a preheated furnace. A rate of "standard" indicates that the standard fire curve was applied for the heating profile. The term "measured" is used for tests where the heating rate was controlled based on measuring the internal temperature of the specimen and maintaining some maximum difference from the furnace temperature. Maximum temperature ("max temp") is recorded as the maximum temperature of the furnace. Exposure "duration" is recorded in hours from the time when heating ends to the time when hot testing or residual cooling begins. An exposure duration of "uniform" indicates the specimen's internal temperature was measured and that heat was applied for a continuous duration until the specimen's internal temperatures uniformly reached the furnace temperature. "Cooling rate" is stated as either "slow" or "rapid". Comprehensive definitions of the two cooling rates are provided in Section 4.4. It should be noted that similar to maximum temperature, the heating and cooling rates refer to the temperature change in the furnace, not the specimen itself. Although the furnace temperature is not necessarily an ideal way to represent these values, it is easier to record and is widely reported in the literature as such.


#### **Table 1.** List of Evaluated Experimental Work with Test Parameters.

#### **4. Influence of Fire Characteristics**

In this section, the influence of each fire characteristic is evaluated. Contrary to the chronological order of a natural fire event, the influence of maximum temperature is discussed first as it is the most well-documented characteristic in the literature. It is intended that by recognizing the effects of maximum temperature first, the less-documented fire characteristics can be subsequently evaluated with greater clarity. ‐

‐

#### *4.1. Influence of Maximum Temperature*

Figure 3 presents the averaged relative strength of hot and residual tests for a range of maximum temperature exposures. The averaged values consist of findings from 37 different studies. To provide an understanding of the variation in existing data, upper and lower limits of the evaluated test data are given (dotted line). Eurocode prescribed strength reductions for siliceous aggregate (dashed line) are also given [34,35].

*‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐* **Figure 3.** Relative strength of concrete for hot and residual conditions. [Includes Tests from T-7A to T-10, T-12 to T-20, T-21A to T-28, T-30 to T-34].

‐ The averaged experimental work shows that increasing maximum temperature has a significant influence on concrete strength. Concrete tested after cooling exhibits lesser strength at every temperature compared with hot tested concrete. This relationship is largely due to the influence of cooling, which is examined in Section 4.4. To address the influence of maximum temperature specifically, discussion focuses on the response of the hot tested profile.

‐ ‐ Concrete strength exhibits three trends when exposed to elevated temperature. At lower temperatures below 350 ◦C, strength loss is relatively minor. Some of the experimental work, such as by Diederichs et al. [14] and Fu et al. [15], even observed moderate strength gains in the low temperature ranges. The extent of these gains can be seen in the steep rise of the dotted upper limit line. Castillo and Duranni [12] proposed that this strength gain results from stiffening of the cement gel due to the evaporation of concrete moisture. As such, changing concrete properties, such as porosity and moisture content, can have a notable impact on delaying strength loss at low maximum temperatures.

In the mid-range temperatures, 350–600 ◦C, strength drops sharply. By 600 ◦C, relative strength levels of 45% and 41% can be expected for hot and residual test averages, respectively. In this temperature range, the concrete becomes substantially dehydrated, such that the full influence of micro-cracking, cement and aggregate decomposition, and thermal expansion stresses is realized [36]. ‐

Above 600 ◦C, severe degradation can be expected, with as much as 90% strength loss by 800 ◦C. This reduction illustrates the substantial influence that maximum temperature has on the strength of concrete. At these higher temperatures, specimens can often be broken up into gravel by hand [37]. The rate of strength loss above 600 ◦C, however, is slightly less severe than in the mid-range temperatures. This lessening rate may be attributed to the calcination or crystallization of aggregates [12]. ‐ ‐

#### *4.2. Influence of Heating Rate*

During concrete heating, a thermal gradient develops between a section's outer layers and inner core. This gradient induces thermal stresses between the different constituents of the concrete, which in turn produces micro-cracking and compressive strength loss. It is by this mechanism that variable rates of heating can influence concrete strength. ‐ ‐

‐

For evaluation, experimental work is divided into low and high heating rates. A low heating rate is defined as a rate less than 3 ◦C/min, with high heating being that greater than 3 ◦C/min. This definition of low and high rates is based off the median heating rate of the available experimental work. For comparison, the standard fire has an average heating rate of 33 ◦C/min (between 0 ◦C and 800 ◦C) and the Cardington fire tests give an average rate of 18 ◦C/min for a typical compartment fire [38]. Although 3 ◦C/min is a comparably much lower rate of heating, the experimental work has focused on this level due to the relative simplicity of its application. These low heating rate tests are also not without merit, as they are still valid for potentially smaller natural fire events. ‐ ‐ ‐ ‐

To control for the effects of the other fire characteristics, only tests with a similar exposure duration have been included. Hot and residual tests have been separated for comparison. All residual tests feature a similar cooling regime. ‐ 

Figures 4 and 5 present the relative concrete strength of hot tested specimens for high and low rates of heating. The average profile for the plotted tests is indicated by the dashed line. The experimental work is found to be in good agreement, with only a few outliers from the test average. Figures 6 and 7 similarly present the relative concrete strength of residually tested specimens. The low heating rate tests show very good agreement, but greater fluctuation is observed for high heating. This may be due to the wider selection of heating rates presented on the plot, ranging from 5 ◦C/min to instantaneous heating. ‐

**Figure 4.** Relative strength of hot tested concrete with high heating rates.

**Figure 5.** Relative strength of hot tested concrete with low heating rates.

**Figure 6.** Relative strength of residually tested concrete with high heating rates.

**Figure 7.** Relative strength of residually tested concrete with low heating rates.

‐ ‐ ‐ Figure 8 records the average strengths of the experimental work for direct comparison. The average profiles have been truncated at 700 ◦C due to a shortage of available tests beyond this temperature. The Eurocode prescribed profiles for hot and residual siliceous concrete are also given as a baseline [34,35].

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**Figure 8.** Relative strength of concrete due to low or high rates of heating.

‐ ‐ Considering the average profiles, no clear trend emerges. In general, high rates appear to result in slightly greater strength reduction. This is most notable for the residually tested concrete at lower temperatures around 200 ◦C. However, at any given temperature, the effect of heating can produce higher, lower, or identical strengths. In particular, beyond 500 ◦C, all four heating regimes converge and result in comparable strength levels.

‐ ‐ ‐ A justification for this minor and fluctuating influence may be due to the conflicting nature of heating mechanisms. At higher heating rates, large thermal gradients develop, causing greater strength reduction due to extensive micro-cracking. However, at the same time, the rapid expulsion of moisture from the concrete strengthens the adhesive action of the cement gel. These two mechanisms act in contrast resulting in similar concrete strengths for low and high heating rates. Mohamidbhai [22] proposed that at temperatures above 600 ◦C, the majority of the moisture is removed, and the micro-cracking occurs regardless of the heating rate. Therefore, low and high rates can be expected to result in similar strength losses at high temperatures, which is reflected in Figure 8.

It should be noted that although heating rate does not have a large impact on concrete strength, it is often cited as having a significant impact on explosive spalling [39]. Explosive spalling is a phenomenon in which exterior portions of a concrete specimen violently spall off during heating. This effect significantly reduces the elements cross-section and potentially exposes internal reinforcement, greatly reducing sectional strength. Castillo and Durrani [12], Noumowe et al. [26], and Phan and Carino [27] all reported major spalling in their high-strength concrete (HSC) samples but none in their NSC. Noumowe et al. [39] observed explosive spalling in HSC specimens at heating rates as low as 1 ◦C/min. It is well documented that NSC is often unaffected by spalling compared with HSC. However, in view of the potential severity of explosive spalling, heating rate is a factor that should be given due consideration.

#### *4.3. Influence of Exposure Duration*

Exposure duration refers to the time for which concrete is subjected to elevated temperatures. For a natural fire, exposure duration would intuitively be taken from the time when the fire starts to when it is fully extinguished. This overall duration, however, is not often reported in the literature. Instead, exposure duration is typically reported as the time from when heating ends to the time when hot testing or residual cooling begins. During this period, the concrete is exposed consistently to the maximum temperature. Defining exposure duration in this way makes temperature control easier during testing. It also has the added benefit of allowing its influence on concrete strength to be separated from that of variable heating and cooling rate. 

‐

‐

To evaluate the influence of exposure duration, this section focuses on the work of Carette et al. [11] and Mohamidbhai [22]. Both studies specifically investigated variable exposure durations, ranging from hours to months. For comparison, complimentary experimental work has been selected with similar heating, residual cooling, calcareous aggregates, and specimen sizes. ‐ ‐ ‐ ‐

Figure 9 presents the relative strength reductions for concrete when exposed to a maximum temperature of 400 ◦C for various durations. Figure 10 provides the same for a 600 ◦C temperature. An exposure duration of "uniform" indicates continuous exposure was applied until the specimen's internal temperatures were measured to match the furnace temperature. An exposure duration of "0-hr" indicates the specimen began cooling immediately after maximum furnace temperature was reached. ‐ ‐ ‐ ‐

**Figure 9.** Relative strength of concrete at 400 ◦C with various exposure durations.

**Figure 10.** Relative strength of concrete at 600 ◦C with various exposure durations.

The results show that the majority of strength loss occurs early in the exposure process. Test T-20 with an exposure duration of 0 h, exhibited relative strength loss of 29% at 400 ◦C and 38% at 600 ◦C.

As exposure duration increases, strength reduction follows two trends. Up until 3 h, moderate strength reduction continues to occur. Beyond 3 h, insignificant further strength reduction is observed. Even at extreme durations of one and four months, strength levels are comparable to the 3 h and 4 h exposure durations. Those two trends are presented in Figures 9 and 10 by the dashed lines.

The rationale behind the relationship can be attributed to the internal temperatures within the concrete. At shorter durations, there is a temperature lag between the outside surfaces of the concrete and the inside. During this period, continued cracking and strength degradation occurs as the internal temperature increases. Once a uniform internal temperature is reached, the mechanisms of strength loss become minimal.

Based on the reviewed experiments, a uniform internal temperature can be expected in typical laboratory test specimens after 3 h of constant exposure. For larger concrete cross-sections, the time it takes to reach a uniform internal temperature varies greatly.

#### *4.4. Influence of Cooling Rate*

As previously observed in Figure 8, the residual strength of concrete after cooling is notably lesser when compared with its hot strength. The cause of this additional strength loss is due to the development of internal temperature gradients, similar to the heating process. Because these gradients form in the opposite direction of heating, they generate new stresses and new cracks that further reduce concrete strength [26].

Considering the effects of a natural environment, variable rates of cooling can be present, ranging from slow cooling in a smoldering compartment to rapid cooling from firefighting efforts. To evaluate the effect of cooling, the reviewed experimental testing is divided into two rates: slow and rapid cooling. In this paper, cooling rate is taken from the time furnace temperature begins to decline until the furnace reaches ambient temperature.

Slow cooling occurs when a test specimen is either cooled within the test furnace or taken outside into the ambient environment. Internal specimen temperature by Lee et al. [19] showed that these two different cooling methods produce very comparable cooling rates. Savaa et al. [30] and Morita et al. [23] indicated that slow cooling results in a rate of 0.4 ◦C/min to 1.0 ◦C/min. Slow cooling can subsequently be defined as having a rate less than or equal to 1.0 ◦C/min.

Rapid cooling is achieved in experimental work by exposing the specimen to water during the cooling stage. Water quenching or spraying techniques are typically applied by submerging or spraying the specimen with ambient temperature water for a prolonged duration. In the specific case of 150 mm cubed specimens, Botte and Caspeele [10] identified that from an elevated temperature of 600 ◦C, quenching is equivalent to a cooling rate of 30–40 ◦C/min. The results of this experiment demonstrate the magnitude of possible cooling rates that can occur during natural fire scenarios.

Figures 11 and 12 display the relative concrete strength of specimens exposed to slow and rapid cooling. Only tests of similar heating rate and exposure duration are presented. All the rapid cooling studies were conducted immediately after cooling was complete, avoiding the influence of potential strength recovery. The overall profile of the experiments for both cooling regimes were found to be in good agreement with one another. Due to the additional inconvenience of conducting rapid cooling tests, their number in the literature is very small.

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**Figure 11.** Relative strength of concrete with slow cooling.

**Figure 12.** Relative strength of concrete with rapid cooling.

‐ ‐ Figure 13 presents the averaged cooling profiles along with the Eurocode siliceous baseline and the averaged profile of the hot tested concrete from Figure 7. It can be seen that an increased cooling rate results in greater strength reduction. Even at a slow rate of cooling, lower residual strengths can be expected when compared with the hot tested specimens. On average, 6% greater strength loss is observed between hot to slow and an additional 10% is observed between slow to rapid.

‐ ‐ ‐ ‐ ‐ ‐ The strength loss due to cooling is not constant with temperature. At low temperatures circa 100 ◦C, the residual concrete exhibits only minorly lesser strength levels as compared with hot tested concrete. However, in the mid-temperature range of 200 ◦C to 500 ◦C, the influence of cooling becomes significant. The maximum difference between hot and rapid cooling is 29% when at 300 ◦C. This trend indicates the extreme importance of considering the influence of cooling rates in moderate fire events. At the higher temperatures above 600 ◦C, the three profiles display some convergence. Due to a shortage of test data, the rapid cooling profile is discontinued early. Specific testing by Lee et al. [19] indicates that at temperatures of 800 ◦C, slow and rapid cooling continue to converge and reach comparable strength levels.

The lack of agreement between the rapid cooling and Eurocode profile should also be noted from Figure 13 [34]. This is the only fire characteristic for which a significant and unconservative relationship is observed between the code and test results. When assessing the residual strength of concrete, this potential limitation in the code prescribed values should be considered.

**Figure 13.** Relative strength of concrete due to slow or rapid cooling.

Post-Fire Strength Recovery Due to Cooling Rate

‐ Post-fire strength recovery is a process by which fire damaged concrete can significantly regain strength when cooled with water. This recovery is attributed to the rehydration of the cement [40]. Maximizing water exposure and allowing time for recuring are important factors in facilitating recovery.

‐ ‐ ‐ The concept of strength recovery has been well investigated in the literature since it was first observed in 1970 by Crook and Murray [41]. Experimental work and reviews often focus on the influence of long-term recuring techniques, such as soaking specimens for weeklong durations [40]. From the perspective of a natural fire event, this duration of water exposure is unlikely. The following experimental work has been reviewed to demonstrate the influence of short-term recuring.

‐ Poon et al. [40] performed experimentation involving a continuation of the test data presented in Table 1 for T-28. After slow air cooling from 600 ◦C, NSC specimens were recured by water spraying for 2 hrs and then tested after 7, 28, and 56 days. The results show that after 7 days, the concrete recovered 14% of its strength, and after 56 days recovered 19%. This represents a significant recovery. The researchers identified that the 2 hr spraying duration was selected after many trials to be the minimum soaking time for optimized results.

‐ ‐ Abramowicz and Kowalski [6] explored the concept of very short duration water cooling. Specimens were either slow cooled in ambient air or rapid cooled by quenching for 10 s, followed by further slow cooling in ambient air. Strength testing was completed the next day. This very short duration immersion and quick testing time produced no significant effect on the specimen's strength compared with the baseline slow cooled specimens.

Based on these findings, rapid water cooling is not sufficient to induce notable strength recovery that is reliably useful for design purposes. This is due to two reasons. Firstly, recuring requires time. When considering the strength of concrete during the natural fire event and the safety of occupants and first responders, insufficient time will have been provided for recuring regardless of water exposure. Secondly, it is important to also consider the geometry of the concrete involved. Far larger amounts of water would be

required for a building, versus 100 mm specimens. To reliably recreate the findings of Poon et al. [40], an extended and intentional recuring effort would be required.

#### **5. Conclusions**

Based on the reviewed literature, the following conclusions can be made regarding the influence of each of the four natural fire characteristics on concrete compressive strength:


The intent of this paper is to provide a general understanding of NSC behaviour during natural fire exposure. This allows designers to focus on the parameters that have the largest impact on concrete behaviour and researchers to identify when newly introduced parameters present unusual responses. To achieve this goal, several assumptions were made which limit the validity of the conclusions of this paper. The reviewed experimental work was limited to: unstressed tests, unconfined tests, unsealed tests, ordinary Portland cement, and NSC. Additionally, other NSC parameters were left uncontrolled and broadly accepted within this review. These parameters include water-cement ratio, aggregatecementitious material ratio, aggregate type, size and content, and geometric dimensions. Future research is needed to address these limitations.

**Author Contributions:** Conceptualization, R.K., M.A.Y. and S.F.E.-F.; data curation, R.K.; investigation, R.K.; writing—original draft preparation, R.K.; writing—review and editing, M.A.Y. and S.F.E.-F.; acquisition, M.A.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC), the India–Canada Center for Innovative Multidisciplinary Partnerships to Accelerate Community Transformation and Sustainability (IC-IMPACTS), and Western University.

**Data Availability Statement:** The data presented in this literature review is available in the referenced papers.

**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relation-ships that could have appeared to influence the work reported in this paper.

#### **References**


## *Article* **Residual Stress-Strain Relationship of Scoria Aggregate Concrete with the Addition of PP Fiber after Fire Exposure**

**Bin Cai <sup>1</sup> , Yu Tao <sup>1</sup> and Feng Fu 2, \***


**Abstract:** Scoria aggregate concrete (SAC) as new green material has been gradually used in some construction projects for its lightweight and high strength, which can reduce the environmental impact of construction materials. In this paper, the residual mechanical properties and intact compressive stress-strain relationships of polypropylene (PP) fiber-reinforced Scoria aggregate concrete after high-temperature exposure at 20, 200, 400, 600, and 800 ◦C were investigated. The failure modes of PP fiber-reinforced Scoria aggregate concrete specimens and the effect of high temperatures on the peak stress, secant modulus, and peak strain were obtained. The results showed that the residual compressive strength of heated concrete is significantly reduced when the temperature exceeds 400 ◦C. The residual strength and residual secant modulus of PP fiber-reinforced Scoria aggregate concrete are significantly higher than those of ordinary concrete. The Scoria aggregate concrete specimens with PP fibers exhibited fewer surface cracks and fewer edge bursts under high temperatures. The residual stress-strain equation of the Scoria aggregate concrete was established by regression analysis, which agreed well with the experimental results.

**Keywords:** Scoria aggregate concrete; PP fiber; high temperature; stress-strain curve

#### **1. Introduction**

With the development of modern building structures with large spans, high rises, and super high rises, concrete that is lightweight, high-strength, and sustainable is needed to lower the structural weight and improve the thermal insulation. Lightweight aggregate concrete has a high quality, is widely used [1], and has long-term performance in buildings [2]. Although it is possible to meet structural strength requirements by using artificial aggregates to make lightweight aggregate concrete, the consumption of materials and energy is often substantial. Therefore, it is important to find natural aggregates with good material properties. Scoria aggregate, which is abundant in Northeast China [3] and is very clean, is one such material. Scoria aggregate concrete is characterized by its high strength, heat insulation, light weight, fire resistance, good deformation performance and low modulus of elasticity [4], and these characteristics can reduce environmental impacts when this material is used in buildings.

Scoria aggregate concrete has excellent compatibility, strength, and water permeability characteristics [5] and good chemical resistance, which enables it to maintain a stable state under acidic conditions with less mass loss [6]. Blocks made from Scoria aggregate concrete are 30–40% lighter in weight than normal concrete with the same strength [7]. As a result, it has wide application prospects [8]. In recent years, the use of this material has increased owing to the increasing demand for environmentally friendly materials and green buildings, and research on it has further developed. Willy H. Juimo Tchamdjou et al. [9] prepared two sets of natural light-aggregate concrete specimens and investigated the performance of Cameroonian Scoria aggregate concrete compared to ordinary lightweight concrete. The

**Citation:** Cai, B.; Tao, Y.; Fu, F. Residual Stress-Strain Relationship of Scoria Aggregate Concrete with the Addition of PP Fiber after Fire Exposure. *Fire* **2021**, *4*, 91. https://doi.org/10.3390/fire4040091

Academic Editor: Maged A. Youssef

Received: 9 November 2021 Accepted: 2 December 2021 Published: 5 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

tests showed that the compressive strength of this concrete increased by 27.42–35.36%, proving that Cameroonian Scoria aggregate concrete can be used as structural concrete. Ahmed A. Abouhussien et al. [10] conducted an experimental study on lightweight slag aggregate concrete and showed that concrete beams mixed with lightweight slag aggregates exhibited higher shear strength compared to normal concrete beams. Kozo Onoue et al. [11] investigated the shock absorption capacity of volcanic pumice lightweight concrete through experiments. The results showed that lightweight concrete had a better damping capacity than the control concrete, which used limestone powder as the coarse aggregate, and was on average 28 and 41% more efficient than the two control concretes in decreasing the maximum impact loads at impact velocities of 1.5 and 4.5 m/s, respectively. J. Alexandre Bogas [12] studied the application of nonstructural lightweight concrete produced using Scoria aggregate in building floor slabs and investigated its mechanical properties. Scoria aggregate concrete containing slag exhibited a similar mechanical strength and better hightemperature properties compared to normal concrete. Aref M. al-Swaidani [13] analyzed the effect of parameters such as the cement content, the Scoria aggregate content, and the water content on other properties by building a neural network model.

Accidental fires are a major cause of durability problems in concrete structures. Aggregate replacement and fiber addition are feasible methods to improve the fire resistance of concrete structures. Generally, concrete structures perform well in fires, but concrete without significant damage may also show a decrease in strength because of an increase in temperature [14]. Therefore, it is important to investigate the reduction in the mechanical properties of concrete after the fire to evaluate and repair fire-damaged concrete elements. At present, the main studies include the basic mechanical properties of lightweight aggregate concrete after exposure to high temperatures and the full stress-strain curve of light-aggregate concrete [15]. Chang, Y. F. et al. [16] conducted an experimental study on the complete stress-strain relationship of concrete after high temperature. The temperature effect on the mechanical properties of the material and the full curve model of stress-strain were obtained by regression analysis. Krzysztof Drozdzol [17] studied the feasibility of using perlite concrete blocks for chimneys. The tests proved that although the thermal loading reduced the compressive strength of the chimney blocks, they still showed an adequate average strength of 4.03 MPa. Shoroog Alraddad [18] analyzed volcanic rocks by temperature difference analysis and thermogravimetric analysis and found that volcanic rocks have good thermal stability and are a highly available and low-cost natural material. Khandaker M. Anwar Hossain [19] studied high-strength Scoria aggregate concrete at 800 ◦C for strength and durability, and compared with a high-strength concrete control, this material showed a better performance in terms of the residual strength, resistance to chloride ion attack, and resistance to high-temperature deterioration. Waqas Latif Baloch [20] studied the effect of incorporation of multi-walled carbon nanotubes on concrete. The results showed that the incorporation of multi-walled carbon nanotubes could improve the strength of concrete both prior to and after exposure to fire. C. Maraveas [21,22] conducted a sensitivity study on the performance of 19th century fireproof flooring systems at high temperatures, and the applicability of the Eurocode expressions to 19th century fireproof flooring systems is satisfactory. Incorporating appropriate amounts of polypropylene (PP) fibers into concrete not only improves the material properties but also enhances its fire resistance and prevents high-temperature bursting [23]. Nicolas Ali Libre et al. [24] tested experimentally the effectiveness of nine mixtures of steel and polypropylene fibers with different volume fractions to improve the ductility of lightweight pumice aggregate concrete. Studies have shown that steel fibers show a very significant improvement in flexural properties, while the improvement in compressive strength is smaller. PP fiber incorporation has little effect on the mechanical properties of concrete. Xi Liu et al. [25] conducted 30 group experiments to investigate whether the incorporation of fibers could positively affect the mechanical properties and axial stress-strain behavior of lightweight confined carbon fiber aggregate concrete. The peak stresses and corresponding strains were modeled and were in good agreement with the experimental results. According to

the test results, the optimum dosing of both steel fiber and carbon fiber is 0.6%. Vahid Afroughsabet [26] investigated the effect of incorporation of steel and polypropylene fiber mixture with 1% volume dose on the mechanical properties and some durability of highstrength concrete. The results showed that the incorporation of 1% volume dose of steel and polypropylene fiber mixture significantly improved the mechanical properties of highstrength concrete. Li Jing Jun et al. [27] analyzed the influence of high-performance PP fibers on the mechanical properties of light-aggregate concrete. It was found that the incorporation of high-performance PP fibers significantly improved their mechanical properties, with an increase in the bending strength, splitting tensile strength, bending toughness, and impact resistance but no significant influence on the compressive strength. To achieve more accurate experimental values in prismatic uniaxial compressive experiments, Liu [28] used the digital image correlation (DIC) method to measure the displacement and strain values of the specimens to obtain their strain clouds, which can reveal phenomena such as regions of crack occurrence and stress concentration. Scoria aggregate concrete has been widely studied because of its many advantages, but the mechanical properties of PP fiber-reinforced Scoria aggregate concrete after exposure to high temperatures and its stress-strain relationship have not been reported.

The purpose of this paper is to obtain the mechanical property and residual stressstrain relationship of Scoria aggregate concrete after high temperature. The data obtained are very important for the design and analysis of building structures, but there are few studies on the stress-strain constitutive relationship of Scoria aggregate concrete after fire exposure. Therefore, we conducted some mechanical tests to obtain the compressive strength and splitting tensile strength of Scoria aggregate concrete after high temperature and measured the residual compressive stress-strain relationship after high-temperature exposure by an advanced DIC system to obtain the changes in peak strain, secant modulus, ultimate strain, and deformation capacity of Scoria aggregate concrete at different temperature exposure levels. In addition, the regression analysis of the experimental results led to the establishment of the constitutive relation equation of Scoria aggregate concrete after high temperature, which provides a reference for the fire design of PP fiber-reinforced Scoria aggregate concrete structures and the evaluation and repair after fire.

#### **2. Experimental Program**

#### *2.1. Materials and Mix Proportion*

The high-strength Scoria aggregate concrete used in this study was designed according to the JGJ51-2002 Technical Specification for Lightweight Aggregate Concrete to produce a design strength grade of C30 and an average density of 1900 kg/m<sup>3</sup> . The mixture proportions are shown in Table 1. Scoria aggregate concrete is made of volcanic slag aggregate, normal Portland cement, styrene–acrylic emulsion, grade II fly ash, PP fibers, and water. The raw material is shown in Figure 1. The porous Scoria aggregate with a bulk density of 815 kg/m<sup>3</sup> was produced in Gushanzi, Huinan County, and artificially pulverized into a continuous gradation of 5~40 mm. The stone for normal concrete is ordinary gravel with a grading size of 5–25 mm, and the sand is ordinary river sand with a fineness modulus of 2.8. P O 42.5 ordinary silicate concrete was used in the mix, initial setting time: 85 min, final setting time: 260 min, compressive strength: 43 MPa (28 days). The bundled monofilament PP fibers had a length of 9 mm, 400 MPa tensile strength, 160 ◦C melting point, and a PP fiber content of 0.22% by volume. Tap water was used for mixing.



W/B = Water/Binder ratio; SA = Scoria aggregate; SAE = Styrene–acrylic emulsion; WRA = Water-reducing admixture.

**Figure 1.** Materials: (**a**) Scoria aggregate, (**b**) PP fiber.

In this paper, three tests were conducted: cube compressive strength, splitting tensile strength, and the axial compressive strength of prismatic with dimensions of 100 mm × 100 mm × 300 mm. A test procedure similar to [29–33] was used. The test specimens for three groups of tests need to be heated to 20, 200, 400, 600, and 800 ◦C. Therefore, a total of 45 specimens of Scoria aggregate concrete and 45 specimens of normal concrete were made for comparison. The prepared test block was placed at room temperature for 24 h and then demolded and cured at 20 ◦C with 95 ± 5% relative humidity for 28 days.

#### *2.2. Test Procedure*

All the following tests were performed in the Structures Laboratory of Jilin Jianzhu University, China. The heating equipment was a resistance furnace with a heating rate of 5 ◦C/min and the temperature in the furnace up to 1000 ◦C. This replicated the standard fire tests [34,35]. After the specimens were heated to 200, 400, 600, and 800 ◦C, the furnace temperature was maintained for 3 h to ensure that the internal temperature of the specimens also reached the target value.

The compressive strength of the cube specimens was tested by a YAR-2000 hydraulic testing machine with a loading rate of 0.5 MPa/s. The axial compressive strength was obtained. Axial compressive tests were performed on the prismatic blocks using a Type YAW-5000 electrohydraulic servo universal testing machine. The testing machine applied load through displacement control and set the loading rate to 0.1 mm/min. The stress was controlled by the test machine, and the strain was measured by DIC. The stress-strain curve was then plotted. The test machine is shown in Figure 2.

**Figure 2.** Testing machine: (**a**) Resistance furnace, (**b**) Hydraulic pressure testing machine, (**c**) DIC.

DIC is a noncontact deformation test method in which marking spots are randomly scattered on a specimen surface, and the changes in the relative positions of these scatter spots during the loading process are compared. The displacement field on the specimen surface was calculated to obtain the strain distribution field for further analysis. A high-

speed camera with a resolution of 1280 × 800 was used for image acquisition. The power of the dimmable LED lamp was 1000 W. The camera was placed symmetrically with the fill light, and the specimen surface with all the scatter spots was placed in the center of the visible range of the camera. The camera was used to photograph the prismatic axial pressure test at a frequency of one photograph per second. The photographs were acquired and analyzed using DIC software to obtain the vertical displacement and transverse strain clouds of the specimen.

#### **3. Test Results and Discussion**

#### *3.1. Failure Mode*

#### 3.1.1. Color Changes

Figure 3 shows the changes in the color and the surface cracks of NC and SAC after exposure to different high temperatures. The specimens changed to yellowish gray, brownish-gray, brown, and whitish gray after being subjected to high temperatures of 200, 400, 600 and 800 ◦C, respectively. Temperatures of 800 and 600 ◦C produced significantly different color changes in the specimens. The Scoria aggregate concrete specimens with PP fibers exhibited fewer surface cracks and less edge bursting after exposure to 800 ◦C. This result may have occurred because the PP fibers melted at 160 ◦C, forming channels through which vapor could diffuse outward and thereby reduce the vapor pressure inside the concrete. These channels were effective in preventing bursting phenomena when the temperature did not exceed 800 ◦C. PP fibers have a melting point of approximately 160 ◦C and were therefore visible inside the specimens at room temperature. When the fire temperature reached 400 ◦C, the PP fibers inside the specimens disappeared.

**Figure 3.** The changes in the color and surface cracks of specimens after high temperatures: (**a**) SAC, (**b**) NC.

#### 3.1.2. Cracking Behavior

Figure 4 shows the maximum crack width on the test block surface after hightemperature treatment, as measured by a fracture-width tester. The maximum crack of Scoria aggregate concrete at 800 ◦C is 0.301 mm, which is 4.43 times higher than that at 200 ◦C. The maximum crack of normal concrete at 800 ◦C is 0.562 mm, which is 5.11 times higher than that at 200 ◦C. The maximum crack width for normal concrete was up to 1.87 times greater than that of the Scoria aggregate concrete.

Figure 5 shows similar patterns of diagonal shear cracking and splitting cracking for the uniaxial compressive damage to the Scoria aggregate concrete specimens treated at different temperatures. The specimens were in the elastic stage at the beginning of loading. The load and displacement increased linearly, and there were no noticeable features on the specimen surfaces. As the load increased, internal microcracks gradually formed, and the specimen stiffness began to decrease. The load increased to a peak, beyond which cracks parallel to the force direction appeared on the surface of the specimens. When

the load was reduced to 60–70% of the peak load, the axial deformation of the concrete block continued to increase and eventually resulted in the destruction of the specimens. The Scoria aggregate concrete specimens showed more noticeable brittle damage than the conventional concrete specimens, with fewer cracks on the specimen surface and less transverse deformation.

**Figure 4.** Maximum crack on the surface of specimens after high temperature: (**a**) SAC, (**b**) NC.

**Figure 5.** Destruction mode of SAC at different temperatures.

#### *3.2. Residual Strength*

By testing the compressive strength and splitting tensile strength of concrete specimens treated at different temperatures, it was concluded that the strength of Scoria aggregate concrete decreases with increasing temperature. The effects of temperature on the compressive strength and the strength reduction coefficients of Scoria aggregate concrete are shown in Table 2.


**Table 2.** Compression strength of specimens after high temperature.

The reduction in compressive strength of Scoria aggregate concrete specimens below 400 ◦C was relatively low, and the compressive strength reduced to 89 and 84% of that at room temperature. However, the reduction in compressive strength of specimens above 400 ◦C was relatively large and the compressive strength reduced to 50 and 27% of that at room temperature. This result was obtained because the hydration products in the specimens gradually decomposed after 450 ◦C, and the thermal mismatch between cement paste and aggregates, resulting in a rapid increase in the number of cracks inside the concrete and a significant decrease in the strength of the specimens. As shown in Figure 6, the compressive strength reduction coefficient of the Scoria aggregate concrete at all temperatures was greater than that of normal concrete, which indicated that the effect of high temperature on the compressive strength of the Scoria aggregate concrete was smaller. The data in Table 2 were fitted to obtain Equations (1) and (2) for the residual axial compressive strengths of SAC and NC after high-temperature treatment.

$$\begin{array}{rcl} f\_{\rm CS,T}/f\_{\rm CS} & = 0.9872 + 0.005142 \left(\frac{T}{100}\right) - 0.0169 \left(\frac{T}{100}\right)^2 \\ & + 0.0006114 \left(\frac{T}{100}\right)^3 20 \, ^\circ \text{C} \le T \le 800 \, ^\circ \text{C} \end{array} \tag{1}$$

$$\begin{array}{rcl} f\_{\text{cn},\text{T}}/f\_{\text{cn}} &= 0.9865 - 0.006324 \left(\frac{T}{100}\right) - 0.01573 \left(\frac{T}{100}\right)^2 \\ &+ 0.0005038 \left(\frac{T}{100}\right)^3 20 \, ^\circ \text{C} \le T \le 800 \, ^\circ \text{C} \end{array} \tag{2}$$

where *f* cs,T and *f* cs are the axial compressive strength of SAC at high temperature and at room temperature, respectively (MPa); *f* cn,T and *f* cn are the axial compressive strength of NC at high temperature and at room temperature, respectively (MPa); and *T* is the temperature, ◦C. The *R* <sup>2</sup> value in Equation (1) is 0.957. The *R* <sup>2</sup> value in Equation (2) is 0.946.

The splitting tensile strengths of the Scoria aggregate concrete after high temperature and its strength reduction coefficients are shown in Table 3. The splitting tensile strength of the Scoria aggregate concrete specimens decreased with increasing temperature to 84, 73, 37, and 22% of the splitting tensile strength at room temperature. Similarly, Figure 7 shows that the splitting tensile strength reduction coefficient of the Scoria aggregate concrete was greater than that of normal concrete at all temperatures. Equations (3) and (4) for the residual axial splitting tensile strength of the specimen were similarly obtained by curve fitting.

$$\begin{aligned} f\_{\rm ts,T}/f\_{\rm ts} &= 0.9902 - 0.009663 \left( \frac{T}{100} \right) - 0.02479 \left( \frac{T}{100} \right)^2 \\ &+ 0.001725 \left( \frac{T}{100} \right)^3 20 \, ^\circ \text{C} \le T \le 800 \, ^\circ \text{C} \end{aligned} \tag{3}$$

$$\begin{array}{rcl} f\_{\text{tn},\text{T}}/f\_{\text{tn}} &= 1.009 - 0.1383 \left(\frac{T}{100}\right) + 0.01342 \left(\frac{T}{100}\right)^2\\ &- 0.001301 \left(\frac{T}{100}\right)^3 20 \text{ } ^\circ \text{C} \le T \le 800 \text{ } ^\circ \text{C} \end{array} \tag{4}$$

where *f* ts,T and *f* ts are the splitting tensile strength of SAC at high temperature and at room temperature, respectively (MPa); *f* tn,T and *f* tn are the splitting tensile strength of NC at high temperature and at room temperature, respectively (MPa), and the *R* <sup>2</sup> value in Equation (3) is 0.961. The *R* <sup>2</sup> value in Equation (4) is 0.931.

**Figure 6.** (**a**) Reduction of compressive strength. (**b**) Relative reduction of compressive strength.

**Table 3.** Splitting tensile strength of specimens after high temperature.


2

**Figure 7.** Splitting tensile strength. (**a**) Reduction of splitting tensile strength. (**b**) Relative reduction of splitting tensile strength.

#### *3.3. Stress-Strain Relationship of Scoria Aggregate Concrete*

#### 3.3.1. Strain Distribution Analysis of DIC

Figure 8 shows the strain distribution from the DIC image of the peak strain and 80% peak strain of the Scoria aggregate concrete at different temperatures. It can be seen that the strain values gradually increased as the temperature increased. As shown in Figure 8b, for the specimen with the lower temperature, when the peak strain was reached, only the transverse strain concentration zone appeared at the bottom of the specimen, and no cracks appeared in the middle of the specimen. For the specimens subjected to higher temperatures, when the peak strain was reached, transverse strain concentration zones appeared at the top and bottom of the specimens, and these strain concentration zones were connected to form cracks, leading to damage of the specimen. The cracks were consistent with the failure mode of the test block in Figure 5, mainly diagonal shear cracking and splitting cracking, as shown in Figure 8h.

**Figure 8.** Strain nephogram of SAC: (**a**) 200 ◦C 80% peak strain; (**b**) 200 ◦C peak strain; (**c**) 400 ◦C 80% peak strain; (**d**) 400 ◦C peak strain; (**e**) 600 ◦C 80% peak strain; (**f**) 600 ◦C peak strain; (**g**) 800 ◦C 80% peak strain; (**h**) 800 ◦C peak strain.

#### 3.3.2. Peak Strain

As shown in Table 4, the peak strains of both normal concrete and Scoria aggregate concrete increased with increasing temperature. However, the change in the peak strain of the Scoria aggregate concrete after high-temperature treatment was smaller than that of normal concrete. The difference between the two peak strains increased significantly above 400 ◦C. The peak strains of normal concrete after exposure to high temperatures were 5.42 and 5.97 times greater than those at room temperature, while the peak strains of the Scoria aggregate concrete after high temperatures were 1.9 and 3.11 times greater than those at room temperature. The excellent fire resistance of the Scoria aggregate concrete specimens resulted in fewer cracks and a smaller peak strain compared to the conventional concrete. The effect of temperature on peak strain is shown in Figure 9. Equations (5) and (6) for the relative peak strain of the specimen were similarly obtained by curve fitting. 2 cps,T cps 3 0.9874 0.08143 0.03687 100 100 0.0007655 20 800 ℃ ℃

$$\begin{aligned} \varepsilon\_{\text{cps},T}/\varepsilon\_{\text{cps}} &= 0.9874 - 0.08143 \left(\frac{T}{100}\right) + 0.03687 \left(\frac{T}{100}\right)^2 \\ &+ 0.0007655 \left(\frac{T}{100}\right)^3 20 \, ^\circ \text{C} \le T \le 800 \, ^\circ \text{C} \end{aligned} \tag{5}$$
 
$$\varepsilon\_{\text{cps},T} = \varepsilon\_{\text{cps},T}$$

$$\begin{array}{rcl} \varepsilon\_{\text{cpn,T}}/\varepsilon\_{\text{cpn}} & = 1.4 - 1.599 \left( \frac{T}{100} \right) + 0.6556 \left( \frac{T}{100} \right)^2 \\ & - 0.04786 \left( \frac{T}{100} \right)^3 20 \, ^\circ \text{C} \le T \le 800 \, ^\circ \text{C} \end{array} \tag{6}$$

where *ε*cps,T and *ε*cps are the peak strain of SAC at high temperature and at room temperature, respectively (MPa); *ε*cpn,T and *ε*cpn are the peak strain of NC at high temperature and at room temperature, respectively (MPa); and the *R* <sup>2</sup> value in Equation (5) is 0.9763. The *R* 2 value in Equation (6) is 0.954. *ε ε ε ε*

**Table 4.** Peak strain of specimens after high temperature.


**Figure 9.** Peak strain of specimens after high temperature: (**a**) Peak strain, (**b**) Relative peak strain.

#### 3.3.3. Secant Modulus

In this paper, the secant modulus corresponding to the rising section of the stress-strain curve of concrete after high temperature from the origin to the 40% peak stress point was taken as the elasticity modulus. Table 5 shows that the secant modulus of the specimens decreased with different degrees of temperature increase, but the secant modulus of Scoria aggregate concrete specimens at different temperatures was greater than that of ordinary concrete. The secant modulus for the Scoria aggregate concrete specimens treated at 200, 400, 600, and 800 ◦C was approximately 70, 30, 13.6, and 3.5% of the secant modulus of the unheated concrete, respectively. The decreasing trend is shown in Figure 10. Equations (7) and (8) for the relative secant modulus of the specimen were obtained by curve fitting.

$$\begin{array}{rcl} \text{S}\_{\text{Cs},\text{T}}/\text{S}\_{\text{cs}} & = 1.045 - 0.1864 \left( \frac{T}{100} \right) - 0.002428 \left( \frac{T}{100} \right)^2 \\ & + 0.001255 \left( \frac{T}{100} \right)^3 20 \, ^\circ \text{C} \le T \le 800 \, ^\circ \text{C} \end{array} \tag{7}$$

$$\begin{array}{rcl} \text{S}\_{\text{cn,T}}/\text{S}\_{\text{cn}} & = 1.04 - 0.1499 \left( \frac{T}{100} \right) - 0.02559 \left( \frac{T}{100} \right)^2 \\ & + 0.003537 \left( \frac{T}{100} \right)^3 20 \text{ } ^\circ \text{C} \le T \le 800 \, ^\circ \text{C} \end{array} \tag{8}$$

2

2

3

3


1.1-0.6517 +0.2525

100

℃ ℃

0.004385 20 800

100 100

100 100

1.105 0.5083 0.1971

100

℃ ℃

where *S*cs,T and *S*cs are the secant modulus of SAC at high temperature and at room temperature, respectively (MPa); *S*cn,T and *S*cn are the secant modulus of NC at high temperature and at room temperature, respectively (MPa), and the *R* <sup>2</sup> value in Equation (7) is 0.9908. The *R* <sup>2</sup> value in Equation (8) is 0.989.

**Table 5.** Secant modulus of specimens after high temperature.


**Figure 10.** Secant modulus of specimens after high temperature: (**a**) Residual secant modulus. (**b**) Relative residual secant modulus.

cus,T cus

cun,T cun

*ε ε*

*ε ε*

#### 3.3.4. Ultimate Strain

The descending section of the stress-strain curve was used to determine the ultimate strain of concrete, corresponding to the strain at the 0.5 *f* cr stress value. The ultimate strain of the specimens after high-temperature treatment is shown in Table 6. The ultimate strain of the concrete increased with temperature, and the amplitude of the variation increased for temperatures above 400 ◦C. The ultimate strains of the Scoria aggregate concrete specimens subjected to temperatures above 400 ◦C were 4.24 and 7.4 times greater than those at room temperature, where the relationship between the temperature and the ultimate strain are shown in Figure 11. Although the ultimate strain reduction coefficient of Scoria aggregate concrete was greater than that of normal concrete, the ultimate strain of Scoria aggregate concrete was still smaller than that of normal concrete even when the temperature reached 800 ◦C because the ultimate strain of Scoria aggregate concrete was very small at room temperature. Equations (9) and (10) for the relative ultimate strain of the specimen were obtained by curve fitting.

$$\begin{array}{rcl} \varepsilon\_{\text{cus,T}}/\varepsilon\_{\text{cus}} & = 1.105 - 0.5083 \left( \frac{T}{100} \right) + 0.1971 \left( \frac{T}{100} \right)^2 \\ & - 0.004385 \left( \frac{T}{100} \right)^3 20 \, ^\circ \text{C} \le T \le 800 \, ^\circ \text{C} \end{array} \tag{9}$$

$$\begin{array}{rcl} \varepsilon\_{\text{cum,T}}/\varepsilon\_{\text{cum}} & = 1.1 - 0.6517 \left( \frac{T}{100} \right) + 0.2525 \left( \frac{T}{100} \right)^2 \\ & - 0.01653 \left( \frac{T}{100} \right)^3 20 \, ^\circ \text{C} \le T \le 800 \, ^\circ \text{C} \end{array} \tag{10}$$

*ε ε*

where *ε*cus,T and *ε*cus are the ultimate strain of SAC at high temperature and at room temperature, respectively (MPa); *ε*cun,T and *ε*cun are the ultimate strain of NC at high temperature and at room temperature, respectively (MPa); and the *R* <sup>2</sup> value in Equation (9) is 0.9996. The *R* <sup>2</sup> value in Equation (10) is 0.993.


**Table 6.** Ultimate strain of specimens after high temperature.

**Figure 11.** Ultimate strain of specimens after high temperature: (**a**) Ultimate strain. (**b**) Relative ultimate strain.

*ε ε*

*ε ε*

#### 3.3.5. Deformation Capacity

Different indicators are used in the literature to quantitatively evaluate the deformation capacity of concrete. The ratio of strain at 50% of the peak stress to the peak strain of concrete (*ε*cu/*ε*cp) was used to evaluate the deformation capacity of the concrete specimens under the action of axial pressure in this study. The larger the ratio is, the higher the deformation capacity of the specimen is. Figure 12 shows how *ε*cu/*ε*cp varies with temperature. Compared to that of the Scoria aggregate concrete, the deformation capacity of the conventional concrete was higher below 400 ◦C and lower (by approximately half) above 600 ◦C. Thus, the Scoria aggregate concrete performed better and had a more stable structure than the conventional concrete under high-temperature conditions. *ε ε ε ε*

*ε ε* **Figure 12.** Effect of temperature on *ε*cu/*ε*cp.

#### **4. Development of Constitutive Equations for Scoria Aggregate Concrete**

#### *4.1. Stress-Strain Curve*

Figure 13 summarizes the axial stress–axial strain curves and axial stress–transverse strain curves of the Scoria aggregate and conventional concrete specimens at different temperatures. Compared to the normal concrete curves, the Scoria aggregate concrete curve has a longer linear ascending section, a steeper descending section (particularly at lower temperatures), and more pronounced brittle damage, which was consistent with the findings of Bing Han [36].

**Figure 13.** stress-strain curve of specimens after high temperature: (**a**) SAC, (**b**) NC.

*ε ε*

Where *ε*<sup>u</sup> is the transverse strain of the specimens and *ε*<sup>v</sup> is the vertical strain of the concrete. The detailed axial stress-strain curves for Scoria aggregate concrete at different fire temperatures are shown in Figure 13b. As the temperature increases, the curve area gradually decreases, and the peak strain moves to the right and increases, whereas the secant modulus decreases sharply. The descending section of the curve is very steep at room temperature, and the curve becomes increasingly flat as the temperature increases. This finding showed that when subjected to high temperatures, Scoria aggregate concrete exhibited better mechanical properties than conventional concrete.

#### *4.2. Constitutive Equations*

Similar normalized stress-strain curves were obtained for the Scoria aggregate concrete and the conventional concrete, and these curves were divided into four stages, as shown in Figure 14.

**Figure 14.** Typical uniaxial compression stress-strain curve of concrete.

*ε* α α Where *ε*c,r is the peak strain, and *f* c,r is the peak stress. In this study, Equation (11) was adopted from the constitutive relation presented in the Code for Design of Concrete Structures (GB50010-2010). The curve consists of ascending and descending sections, the shapes of which are controlled by the independent parameters *n* and *α*, respectively. As shown in Equation (12), the parameter *n* is identified by peak strain, the secant modulus, and peak stress of concrete, and reflects the stress-strain curve characteristics of the rising section of concrete. The parameter *α* determines the stress-strain curve characteristics of the falling section of concrete. The larger the value of *α*, the steeper the descending section of the stress-strain curve. The change in the magnitude of *α* value can reflect the changing characteristics of the concrete stress-strain curve. The concrete plastic deformation properties deteriorate as *α* increases.

$$\begin{cases} \ y = n\mathbf{x}/n - 1 + \mathbf{x}^n & \mathbf{x} \le 1 \\\ y = \mathbf{x}/n(\mathbf{x} - 1)^2 + \mathbf{x} & \mathbf{x} \ge 1 \end{cases} \tag{11}$$

where *x* = *ε*/*εc*,*<sup>r</sup>* , *y* = *σ*/ *fc*,*<sup>r</sup>* .

= ⁄, = ⁄,.

$$n = E\_{\mathfrak{c}} \varepsilon\_{\mathfrak{c},r} / E\_{\mathfrak{c}} \varepsilon\_{\mathfrak{c},r} - f\_{\mathfrak{c},r}. \tag{12}$$

= , ,, The experimental data were regressed to obtain *n* and *α* for the Scoria aggregate concrete at different fire temperatures. The results are shown in Table 7. Figure 15 is a comparison of Equations (11) and (12) with the experimental curves that were used to validate the proposed constitutive model. In the ascending phase, the normalized stressstrain curves at different temperatures have nearly the same shape with only slight changes

in *n*. The descending phase is very steep at lower temperatures, where the Scoria aggregate concrete was brittle and had poor ductility. The *α* value was large at lower temperatures and gradually decreased as the temperature increased. The *R* <sup>2</sup> value reached approximately 0.8. Thus, the constitutive model effectively reproduced the complete test stress-strain curve.

**Table 7.** Equation parameters of stress-strain curves of SAC after elevated temperatures.


**Figure 15.** Comparison between calculated and tested curves of HPLWC after different temperatures: (**a**) Ambient temperature, (**b**) 200 ◦C, (**c**) 400 ◦C, (**d**) 600 ◦C, (**e**) 800 ◦C.

#### **5. Conclusions**

After sorting and comparing the data obtained, the following conclusions related to the residual mechanical properties of Scoria aggregate concrete after fire exposure can be made.

(1) The specimens turned yellowish gray, brownish-gray, brown, and whitish gray after being subjected to temperatures of 200, 400, 600, and 800 ◦C, respectively. The incorporation of the PP fibers effectively prevented bursting phenomena when the temperature did not exceed 800 ◦C.

(2) The effect of temperature on the maximum crack width was significant, with the maximum crack width of SAC at 800 ◦C being 4.43 times that at 200 ◦C. The maximum crack width of the normal concrete was much larger than that of the PP fiber-reinforced Scoria aggregate concrete, reaching a value that was 1.87 times greater than that of Scoria aggregate concrete at 800 ◦C.

(3) The temperature significantly affected the damage mode of the PP fiber-reinforced Scoria aggregate concrete. Strength reductions began to increase above 400 ◦C (an important demarcation point). After 200 ◦C, the PP fiber-reinforced Scoria aggregate concrete retained approximately 89% of its unheated compressive strength, which was further reduced to 50 and 27% after exposure to temperatures of 600 and 800 ◦C, respectively.

(4) The compressive strength reduction coefficient of Scoria aggregate concrete at 800 ◦C was 0.27, while the compressive strength reduction coefficient of the normal concrete after 800 ◦C was 0.2. The degradation of the secant modulus caused by high temperatures was more serious than the degradation of the residual strength, and the secant modulus reduction coefficient of Scoria aggregate concrete at 800 ◦C was 0.035, while the secant modulus reduction coefficient of the normal concrete after 800 ◦C was 0.021.

(5) The deformation capacity of the PP fiber-reinforced Scoria aggregate concrete at 600 and 800 ◦C was generally better than that of the normal concrete, and at 200 and 400 ◦C, the deformation capacity of the PP fiber-reinforced Scoria aggregate concrete was lower than that of the normal concrete. However, PP fiber-reinforced Scoria aggregate concrete has better mechanical properties compared to normal concrete at high temperatures.

(6) Mathematical expressions for the full stress-strain curve of Scoria aggregate concrete were established based on *n* and *α*, and these expressions can be used to numerically simulate the intrinsic structural relationship of Scoria aggregate concrete, as in the present study.

**Author Contributions:** Conceptualization, B.C. and F.F.; methodology, B.C. and F.F.; test, Y.T.; validation, Y.T.; investigation, Y.T.; resources, B.C.; data curation, B.C.; writing—original draft preparation, Y.T.; writing—review and editing, Y.T.; visualization, B.C.; supervision, B.C.; project administration, B.C.; funding acquisition. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the scientific research projects of the Education Department of Jilin province, grant number JJKH20210279KJ.National Natural Science Foundation of China, 51968013.

**Conflicts of Interest:** The authors declare that they have no competing interests.

#### **References**

